Explanation:
Step I: [Take only first 5 digits] A five digit number divisible by 5 can only end with '5'(0 is not allowed)
=> Middle digit is 5. Number is _ _ _ _ 5 _ _ _ _
Step II: All even digits should be even. because they'll be divided by an even number.
Step III: [Take only first 8 digits]An eight digit number with 6th digit as even number, last 2 digit can have only 4 combinations, . These are 96, 16, 72, 32. Number will be as follows:
(EDIT: Considering that it is divisible by 8 and 7th digit is odd)
_ _ _ _ 5 _ 1 6 _
_ _ _ _ 5 _ 9 6 _
_ _ _ _ 5 _ 7 2 _
_ _ _ _ 5 _ 3 2 _
Step IV: [Take only first 4 digits]A four digit number divisible by four ends only with 2 or 6. Keeping in mind that these number don't repeat only 4 Combinations are possible:
(EDIT: Using the fact that 3rd digit is odd and is divisible by 4)
_ _ _ 2 5 _ 1 6 _
_ _ _ 2 5 _ 9 6 _
_ _ _ 6 5 _ 7 2 _
_ _ _ 6 5 _ 3 2 _
Step V: [Take only first 6 digits]For a number to be divisible by 6; 6th number should be even and last three digit should add up to make a multiple of 3. Only 4 Combinations possible
_ _ _ 2 5 8 1 6 _
_ _ _ 2 5 8 9 6 _
_ _ _ 6 5 4 7 2 _
_ _ _ 6 5 4 3 2 _
Step VI: Now only one even number is remaining for occupying 2nd place in each of the above combination. For example in Ist case: 4 is the only remaining even number to be consumed. The combination will go as follows:
_ 4 _ 2 5 8 1 6 _
_ 4 _ 2 5 8 9 6 _
_ 8 _ 6 5 4 7 2 _
_ 8 _ 6 5 4 3 2 _
Step VII: Total 10 combinations remain:
1 4 9 2 5 8 1 6 _
9 4 1 2 5 8 9 6 _
3 8 1 6 5 4 7 2 _
1 8 3 6 5 4 3 2 _
3 8 1 6 5 4 7 2 _
1 8 3 6 5 4 3 6 _
1 8 9 6 5 4 7 2 _
9 8 1 6 5 4 3 2 _
1 8 9 6 5 4 7 2 _
9 8 1 6 5 4 3 2 _
Step VIII: Taking only first 7 digits of all of the above numbers. Only 3816547 is divisible by Seven
Complete number 381654729 is divisible by 9.
I am sure only 381654729 thus satisfies the answer.
Feel free to correct me if im work